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Nonlinear Method for Noisy Signals Full Recovery with Wavelet-Transformation

Keywords:

A. A. Balagur, O. A. Mikhalin, A.A. Khrustalev


In the study of no stationary signals that have no explicit periodic nature, the most effective is the use of localized time-compact bases. Wavelets - this is the mathematical functions which are used to analyze the various frequency components of the data. In the radio transmission of information theory and wavelet analysis applied to solving several important problems, such as the speech signal, the restoration of noisy signals. For the nonlinear noise using wavelet transform has consistently applied the following procedure: direct wavelet transform; zeroing insignificant coefficients of the transformation of the threshold level proportional to the amplitude of the noise; inverse wavelet transform. Nonlinear method, the removal of noise is that the orthogonal wavelet transform «compress» a signal to a large number of relatively large coefficients. As the «white» noise in any orthogonal transformation preserves its structure and the amplitude and the wavelet coefficients are constant, the threshold cutoff not significant coefficients of wavelet transform greatly reduces the noise without affecting the structure of the signal. To restore the signal you need to apply inverse wavelet transform. To conduct the experiment we created a virtual device for non-linear reconstruction noise signal by using wavelet transform, developed in the LabVIEW programming environment and allow you to restore the noisy signal. This method of recovery is most effective when you remove the white noise. «White» noise in any orthogonal transformation preserves its structure and the amplitude and the wavelet coefficients are constant. Nonlinear circumcision irrelevant coefficients of wavelet transform removes the noise while not affecting the structure of the signal. The essence of this admission is that different scale versions of the signal (multiscale edge detection) are transformed in different ways: very sharp changes in the amplitude corresponding to the useful signal, there are still almost unchanged, while the much smaller amplitude noise becomes vanishing small. In the study of no stationary signals that have no explicit periodic nature, the most effective is the use of localized time-compact bases. In the radio transmission of information theory and wavelet analysis applied to solving several important problems, such as the speech signal, the restoration of noisy signals. The proposed method of nonlinear (threshold), the removal of noise is that the orthogonal wavelet transform «compress» signal to a small number of large coefficients. This method of recovery is most effective when you remove the white noise. Nonlinear circumcision irrelevant coefficients of wavelet transform removes the noise while not affecting the structure of the signal.
References:
June 24, 2020
May 29, 2020

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